We consider quantum-mechanical probabilities of bremsstrahlung of photons in the case of low-energy Coulomb collisions in a magnetic field, where the scattering center so perturbs the state of the incident electron that the motion of the latter becomes quasi-bound. Quantum formulas for the spectral power of bremsstrahlung radiation are obtained from the classical formulas by replacing the Fourier amplitudes of the particle velocity with matrix elements of the velocity operator for wave functions, which are normalized by the condition of a unit flux being incident on the nucleus (or an equivalent outgoing flux), with summation over finite Landau levels and quantized values of the impact parameter. Equivalent forms of the specified matrix elements, which are expressed in terms of the Coulomb field and annihilation/creation operators for the eigenfunctions of the operator of the squared impact parameter, are presented. The obtained presentations for the spectral power of bremsstrahlung radiation in the case of quasi-bound electron motion allow one to translate the results of calculating this value in the classical limit to the quantum case, which is typical of white dwarfs with the strongest magnetic fields.
Similar content being viewed by others
References
H. Friedrich and D. Wintgen, Phys. Rep., 183, 37 (1989).
D. T. Wickramasinghe and L. Ferrario, Publ. Astron. Soc. Pacific, 112, 873 (2000).
L. Ferrario, D. de Martino, and B.T. Gänsicke, Space Sci. Rev., 191, 111 (2015).
V. V. Zheleznyakov, Radiation in Astrophysical Plasma [in Russian], Janus-K, Moscow (1997).
V. V. Zheleznyakov, S. A. Koryagin, and A.V. Serber, Astron. Lett., 25, 437 (1999).
S.C. West, Astrophys. J., 345, 511 (1989).
D. Delande, A. Bommier, J.C. Gay, Phys. Rev. Lett., 66, 141 (1991).
N. Merani, J. Main, and G. Wunner, Astron. Astrophys., 298, 193 (1995).
A. Y. Potekhin, G.G. Pavlov, and J. Ventura, Astron. Astrophys., 317, 618 (1997).
L. B. Zhao and P.C. Stancil, Phys. Rev. C, 74, No. 5, 055401 (2006).
L. B. Zhao and P.C. Stancil, Astrophys. J., 667, 1119 (2007).
O.Chuluunbaatar, A.A. Gusev, V. L. Derbov, et al., J. Phys. A, 40, 11485 (2007).
O. Chuluunbaatar, A.A. Gusev, S. I. Vinitsky, et al., Phys. Rev. C, 77, No. 3, 034702 (2008).
L.D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Pergamon, Oxford (1991).
S. A. Koryagin, Radiophys. Quantum Electron., 51, 462 (2008).
S. A. Koryagin, Radiophys. Quantum Electron., 51, 616 (2008).
S. Chandrasekhar and F.H. Breen, Astrophys. J., 104, 430 (1946).
O.-A. Al-Hujaj and P. Schmelcher, Phys. Rev. C, 61, No. 6, 063413 (2000).
V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasmas, Pergamon Press, Oxford (1970).
I. I. Bubukina and S.A. Koryagin, J. Exp. Theor. Phys., 108, 917 (2009).
S. A. Koryagin, Radiophys. Quantum Electron., 56, 664 (2014).
S. A. Arsenyev and S.A. Koryagin, Radiophys. Quantum Electron., 53, 650 (2010).
G.G. Pavlov and I.A. Shibanov, Sov. Astron., 22, 214 (1978).
G. G. Pavlov and A.N. Panov, J. Exp. Theor. Phys., 44, 300 (1976).
M.H. Johnson and B.A. Lippmann, Phys. Rev., 76, 828 (1949).
L. Landau, Z. Phys., 64, 629 (1930).
A. Messiah, Quantum Mechanics, Dover Publ., New York (2014).
A. A. Sokolov and I. M. Ternov, Radiation from Relativistic Electrons, Amer. Inst. Phys., New York (1986).
M. Abramowitz and I. Stegun (eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards (1972).
A. Sommerfeld, Atombau und Spektrallinien, Bd. 2, Friedr. Vieweg. Sohn., Braunschweig (1951).
V. B. Berestetskii, L. P. Pitaevskii, and E.M. Lifshitz, Quantum Electrodynamics, Butterworth-Heinemann, Oxford (2008).
L. A. Weinstein, Electromagnetic Waves, Radio i Svyaz’, Moscow (1988).
G. Bekefi, Radiation Processes in Plasmas, Wiley, New York (1966).
S. A. Arsenyev and S.A. Koryagin, J. Exp. Theor. Phys., 114, 913 (2012).
L.P. Gor’kov and I.E. Dzyaloshinskii, Sov. Phys. JETP, 26, 449 (1968).
P. Schmelcher and L. S. Cederbaum, Phys. Rev. A, 43, 287 (1991).
A. Y. Potekhin, J. Phys. B, 27, 1073 (1994).
A. Y. Potekhin and D. Lai, Mon. Not. Roy. Astron. Soc., 376, 793 (2007).
A. Y. Potekhin, Astron. Astrophys., 518, A24 (2010).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 60, No. 3, pp. 191–207, March 2017.
Rights and permissions
About this article
Cite this article
Koryagin, S.A., Balandin, I.A. Probabilities of Bremsstrahlung Emission of Photons at Low-Energy Electron-Nuclear Collisions in a Magnetic Field. Radiophys Quantum El 60, 171–185 (2017). https://doi.org/10.1007/s11141-017-9788-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11141-017-9788-9